Loading up the data for some preliminary analyses of the binary
climb/no-climb categories.
Load data
Note that the indices are all caps, and the linear measurements have
lowercase letters after the first.
dat <- read_sheet("https://docs.google.com/spreadsheets/d/1-eknhyZ1JNnXqhg2kViyzVntC8NGZvILQX-aQQb1Jvk/edit#gid=325036460", na = c("NA", "?", "")) %>%
select(!NOTES) %>%
# Recode Ordinal Rankings
mutate(Loc_Ord = case_when(Loc_mode_Ordinal == "G" ~ 1,
Loc_mode_Ordinal == "A" ~ 2,
Loc_mode_Ordinal == "Sc" ~ 3,
Loc_mode_Ordinal == "T" ~ 4,
Loc_mode_Ordinal == "Is" ~ 5,
Loc_mode_Ordinal == "Sf" ~ 5,
Loc_mode_Ordinal == "Ss" ~ 6,
TRUE ~ NA),
Loc_Ord = as.ordered(Loc_Ord),
Loc_bin = case_when(Loc_mode_Bindary == "Ground" ~ 0,
Loc_mode_Bindary == "Tree" ~ 1,
TRUE ~ NA
),
# Loc_bin = as.factor(Loc_bin),
Loc_mode_Categorical = as.factor(Loc_mode_Categorical),
log_Mass = log(Mass_grams)) %>%
relocate(Loc_bin, .after = Loc_mode_Bindary) %>%
relocate(Loc_Ord, .after = Loc_mode_Ordinal) %>%
relocate(log_Mass, .before = Skl) %>%
#Calculate Ratios
mutate(SI = Sh / Sl, # Scapular Index
HRI = Hsw / Hl, # Humeral Robustness Index
HPI = Hpw / Hl, # Humeral Proximal Index
HEB = Hdw / Hl, # Humeral Epicondyle Breadth
HHRI = Hhl / Hl, # Humeral Head Robustness Index
HHW = Hhw / Hhl, # Humeral Head Shape Index
DI = Hdcw / Hsw, # Deltopectoral Crest Index
OLI = Uol / Ul, # Olecranon Process Length Index
BI = Rl / Hl, # Brachial Index
IM = (Hl+Ul)/(Fl+Tl), # Intermembral Index
PRTI = Mcl/(Hl+Rl), # Palm Robustness Index
MRI = Mcw / Mcl, # Metacarpal Robustness
MANUS = Ppl / Mcl, # MANUS index
MANUS2 = (Ppl+Ipl)/Mcl, # MANUS index with intermed. phalanx
IRI = Fgh / Fl, # Gluteal Index
FRI = Fsw / Fl, # Femoral Robustness
FEB = Fdw / Fl, # Femoral Epicondyle Breadth
CI = Tl / Fl, # Crural Index
TRI = Tmw / Tl, # Tibial Robustness Index
#ANR = Anl / Al, # Astragular Neck Robustness Index
#CAR = Cal / Cl, # Calcaneal Robustness Index
IRI = Il / Pel, # Illium Robustness Index
PR = Il / Isl, # Pelvic Index
PES = Pppl / Mtl, # PES INdex
PES2 = (Pppl+Pipl)/Mtl # PES with intermediate Phalanx
) %>%
mutate_at(vars(17:71), log) %>%
mutate_at(vars(16:93), scale2)
✔ Reading from Master_Data.
✔ Range all data.
What does the missing data look like?
You can scroll through the table below
n = nrow(dat)
dat %>% select(16:93) %>%
summarise_all((~ sum(is.na(.)))) %>%
mutate_if(is.double, ~ n - .) %>%
pivot_longer(everything(), names_to = "measurement", values_to = "count_missing") %>% arrange(desc(count_missing), measurement) %>%
mutate(percent_missing = round(count_missing / n, digits = 3)) %>%
kbl(caption = "Percentage of Missing Data") %>%
kable_classic(full_width = F, html_font = "Cambria") %>%
scroll_box(width = "500px", height = "200px")
Percentage of Missing Data
| measurement |
count_missing |
percent_missing |
| Pdpw |
324 |
0.773 |
| Pipw |
278 |
0.663 |
| Pdpl |
277 |
0.661 |
| Dpw |
263 |
0.628 |
| Jl |
249 |
0.594 |
| Anl |
239 |
0.570 |
| Atw |
239 |
0.570 |
| Cal |
239 |
0.570 |
| Ccw |
238 |
0.568 |
| Csw |
238 |
0.568 |
| Ctl |
238 |
0.568 |
| Ctw |
238 |
0.568 |
| Al |
237 |
0.566 |
| Pppw |
230 |
0.549 |
| Skl |
228 |
0.544 |
| Mtw |
223 |
0.532 |
| Ipw |
217 |
0.518 |
| Dpl |
216 |
0.516 |
| PES2 |
194 |
0.463 |
| Pipl |
193 |
0.461 |
| Fbdw |
189 |
0.451 |
| Fbmw |
187 |
0.446 |
| Fgh |
187 |
0.446 |
| Fhd |
187 |
0.446 |
| HHRI |
185 |
0.442 |
| HHW |
185 |
0.442 |
| Hhl |
185 |
0.442 |
| Hhw |
185 |
0.442 |
| Ppw |
158 |
0.377 |
| Cl |
154 |
0.368 |
| Fbpw |
153 |
0.365 |
| MRI |
152 |
0.363 |
| Mcw |
152 |
0.363 |
| DI |
144 |
0.344 |
| Hdcw |
144 |
0.344 |
| Tdw |
141 |
0.337 |
| Tpw |
138 |
0.329 |
| Fbl |
137 |
0.327 |
| IRI |
137 |
0.327 |
| Isl |
137 |
0.327 |
| PR |
137 |
0.327 |
| Pel |
137 |
0.327 |
| Il |
136 |
0.325 |
| HPI |
135 |
0.322 |
| Hpw |
135 |
0.322 |
| Ipl |
117 |
0.279 |
| MANUS2 |
117 |
0.279 |
| PES |
95 |
0.227 |
| Pppl |
94 |
0.224 |
| Mtl |
88 |
0.210 |
| MANUS |
23 |
0.055 |
| Ppl |
23 |
0.055 |
| Mcl |
17 |
0.041 |
| PRTI |
17 |
0.041 |
| log_Mass |
10 |
0.024 |
| TRI |
3 |
0.007 |
| Tmw |
3 |
0.007 |
| CI |
2 |
0.005 |
| FEB |
2 |
0.005 |
| Fdw |
2 |
0.005 |
| IM |
2 |
0.005 |
| Tl |
2 |
0.005 |
| FRI |
1 |
0.002 |
| Fl |
1 |
0.002 |
| Fsw |
1 |
0.002 |
| SI |
1 |
0.002 |
| Sh |
1 |
0.002 |
| Sl |
1 |
0.002 |
| BI |
0 |
0.000 |
| HEB |
0 |
0.000 |
| HRI |
0 |
0.000 |
| Hdw |
0 |
0.000 |
| Hl |
0 |
0.000 |
| Hsw |
0 |
0.000 |
| OLI |
0 |
0.000 |
| Rl |
0 |
0.000 |
| Ul |
0 |
0.000 |
| Uol |
0 |
0.000 |
Binary Climb/No Climb Models
Preliminary data analysis, looping over all of the variables to see
which ones do a good job predicting the binary tree vs. no-tree
categorization
These are very preliminary data, and the results will become more
Here are all the model plots. On the y axis, 1 is TREE, 0 is NO TREE.
The x axis is the phenotype, mean centered on 0 and scaled to a standard
deviation of 1. All of the linear measurements are log transformed prior
to mean-centering. All the models include log_mass as a variable,
meaning that they are “size corrected”
representations of the effect of the phenotype on climbing. What we are
looking for is a slope that ranges across the whole y axis, meaning that
it touches the 1 and 0, and has a steep slope (either up or down). To
interpret, look at the 3rd plot, Hl. As Hl increases,
the probability of being TREE increases.
Here are some standouts: (remember, these are log-transformed
and size-corrected effect sizes)
- humeral length (Hl)
- Olecranon length (Uol)
- Ulnar length (Ul)
- Radius length (Rl)
- Femur length (Fl)
- Proximal phalanx of the manus length (Ppl)
- Intermediate phalanx of the manus length (Ppl)
- Olecranon Length Index (OLI)
- MANUS and MANUS2 indices (#2 includes the intermediate phalanx)
- PES and PES2
for(i in fit_list2){
plot <- plot(conditional_effects(i), plot=F, points = T)[[1]]
print(plot)
}











































































---
title: "First Glimpse of Data"
output: html_document
---

Loading up the data for some preliminary analyses of the binary climb/no-climb categories.

```{r message = FALSE, warning=FALSE, include = FALSE}
pacman::p_load(tidyverse, googlesheets4, brms, cmdstanr, kableExtra)
options(brms.backend = "cmdstanr")

scale2 <- function(x, na.rm = TRUE) (x - mean(x, na.rm = TRUE)) / sd(x, na.rm)
```

#### Load data  

Note that the indices are all caps, and the linear measurements have lowercase letters after the first.

```{r}
dat <- read_sheet("https://docs.google.com/spreadsheets/d/1-eknhyZ1JNnXqhg2kViyzVntC8NGZvILQX-aQQb1Jvk/edit#gid=325036460", na = c("NA", "?", "")) %>%
  select(!NOTES) %>% 
# Recode Ordinal Rankings
  mutate(Loc_Ord = case_when(Loc_mode_Ordinal == "G" ~ 1,
                             Loc_mode_Ordinal == "A" ~ 2,
                             Loc_mode_Ordinal == "Sc" ~ 3,
                             Loc_mode_Ordinal == "T" ~ 4,
                             Loc_mode_Ordinal == "Is" ~ 5,
                             Loc_mode_Ordinal == "Sf" ~ 5,
                             Loc_mode_Ordinal == "Ss" ~ 6,
                             TRUE ~ NA),
         Loc_Ord = as.ordered(Loc_Ord),
         Loc_bin = case_when(Loc_mode_Bindary == "Ground" ~ 0,
                             Loc_mode_Bindary == "Tree" ~ 1,
                             TRUE ~ NA
                             ),
        # Loc_bin = as.factor(Loc_bin),
         Loc_mode_Categorical = as.factor(Loc_mode_Categorical),
         log_Mass = log(Mass_grams)) %>% 
    relocate(Loc_bin, .after = Loc_mode_Bindary) %>% 
  relocate(Loc_Ord, .after = Loc_mode_Ordinal) %>% 
  relocate(log_Mass, .before = Skl) %>% 
#Calculate Ratios
  mutate(SI = Sh / Sl,             # Scapular Index
         HRI = Hsw / Hl,           # Humeral Robustness Index
         HPI = Hpw / Hl,           # Humeral Proximal Index
         HEB = Hdw / Hl,           # Humeral Epicondyle Breadth
         HHRI = Hhl / Hl,          # Humeral Head Robustness Index
         HHW = Hhw / Hhl,          # Humeral Head Shape Index
         DI = Hdcw / Hsw,          # Deltopectoral Crest Index
         OLI = Uol / Ul,           # Olecranon Process Length Index
         BI = Rl / Hl,             # Brachial Index
         IM = (Hl+Ul)/(Fl+Tl),     # Intermembral Index
         PRTI = Mcl/(Hl+Rl),       # Palm Robustness Index
         MRI = Mcw / Mcl,          # Metacarpal Robustness
         MANUS = Ppl / Mcl,        # MANUS index
         MANUS2 = (Ppl+Ipl)/Mcl,   # MANUS index with intermed. phalanx
         IRI = Fgh / Fl,           # Gluteal Index
         FRI = Fsw / Fl,           # Femoral Robustness
         FEB = Fdw / Fl,           # Femoral Epicondyle Breadth
         CI = Tl / Fl,             # Crural Index
         TRI = Tmw / Tl,           # Tibial Robustness Index
         #ANR = Anl / Al,          # Astragular Neck Robustness Index
         #CAR = Cal / Cl,          # Calcaneal Robustness Index
         IRI = Il / Pel,           # Illium Robustness Index
         PR = Il / Isl,            # Pelvic Index
         PES = Pppl / Mtl,         # PES INdex
         PES2 = (Pppl+Pipl)/Mtl    # PES with intermediate Phalanx
         ) %>% 
  mutate_at(vars(17:71), log) %>% 
  mutate_at(vars(16:93), scale2)
```
What does the missing data look like?  
You can scroll through the table below  

```{r }
n = nrow(dat)

dat %>% select(16:93) %>% 
  summarise_all((~ sum(is.na(.)))) %>% 
  mutate_if(is.double, ~ n - .) %>% 
  pivot_longer(everything(), names_to = "measurement", values_to = "count_missing") %>% arrange(desc(count_missing), measurement) %>% 
  mutate(percent_missing = round(count_missing / n, digits = 3)) %>% 
  kbl(caption = "Percentage of Missing Data") %>% 
  kable_classic(full_width = F, html_font = "Cambria") %>% 
  scroll_box(width = "500px", height = "200px")
```


#### Binary Climb/No Climb Models

Preliminary data analysis, looping over all of the variables to see which ones do a good job predicting the binary tree vs. no-tree categorization

These are very preliminary data, and the results will become more 

```{r message = FALSE, warning=FALSE, include = FALSE, cache=TRUE}
#initial fit
mm <- brm(
  #Loc_bin ~ Sl + log_Mass + (1 | Genus_species),
  Loc_bin ~ Sl + log_Mass,
           family = bernoulli(),
           data = dat, refresh = 0)
```


```{r message = FALSE, warning=FALSE, include = FALSE, cache=TRUE}

varis <- colnames(dat)[19:93]

fit_list <- vector(mode ="list", length = 77)

for(i in varis){
  fit_list[[i]]<- update(mm,
                         #formula=(paste0("Loc_bin ~", i, "+log_Mass+(1|Genus_species)")),
                         formula=(paste0("Loc_bin ~", i, "+log_Mass")),
                         family = bernoulli(),
                         newdata=dat,
                         refresh = 0
                         ) 
}

fit_list2 <- fit_list[78:152]
rm(fit_list)
```

Here are all the model plots. On the y axis, 1 is TREE, 0 is NO TREE. The x axis is the phenotype, mean centered on 0 and scaled to a standard deviation of 1. All of the linear measurements are log transformed prior to mean-centering. All the models include log_mass as a variable, meaning that they are "***size corrected***" representations of the effect of the phenotype on climbing. What we are looking for is a slope that ranges across the whole y axis, meaning that it touches the 1 and 0, and has a steep slope (either up or down). To interpret, look at the 3rd plot, **Hl**. As Hl increases, the probability of being **TREE** increases. 

Here are some standouts: (**remember, these are log-transformed and size-corrected effect sizes**)  

- humeral length (Hl)  
- Olecranon length (Uol)  
- Ulnar length (Ul)  
- Radius length (Rl)  
- Femur length (Fl)  
- Proximal phalanx of the manus length (Ppl)  
- Intermediate phalanx of the manus length (Ppl)  
- Olecranon Length Index (OLI)  
- MANUS and MANUS2 indices (#2 includes the intermediate phalanx) 
- PES and PES2  

```{r message = FALSE, warning=FALSE, cache=TRUE}
for(i in fit_list2){
 plot <- plot(conditional_effects(i), plot=F, points = T)[[1]]
 print(plot)
}

```
